G.B. Bruna FRAMATOME ANP

1. PWR Nuclear Reactor Core DesignPower and Reactivity Elements on Reactor Kineticsand Residual Power G.B. Bruna FRAMATOME ANP

2. Foreword • Neutron Balance Equation of a multiplying system at time t:

3. Foreword • Steady State Conditions • At any time t :

4. Foreword • Steady State Conditions • At any time t : • The number of neutron in any generation equals the number of neutrons in the previous and following generation; • The prompt-neutron lifetime equals exactly the generation-time .

5. Foreword • Steady State Conditions • At any time t, any explicit dependence on the variable time can be dropped out :

6. Foreword • Steady State Conditions • In steady state conditions, the neutron balance of the system changes • Very slightly due to: • Xenon oscillations, • Fuel burn-out, • With a time-constant which is quite long against observation-time.

7. Power and Reactivity • Main Parameters in Reactor Core Design • Power • It is a physical observable which measures the energy released under different forms (kinetic energy of fission fragments, kinetic energy of fission neutrons, gamma) within the system by neutron fission, capture and slowing-down. • Reactivity • It is not a real physical observable because it measures the reset that is to be applied to the fission operator to restore criticality of a given multiplying system, generally not critical after any perturbation (change of the state Boltzmann operator).

8. Power and Reactivity • Power • Total Fiss Power • Total Power • Local Fiss Power

9. Power and Reactivity • Power • Power Peak • Axial Offset

10. Power and Reactivity • Reactivity

11. Power and Reactivity • Control of Power • Power distribution within the reactor core is not flat because of : • Neutron gradient (leakage), • Short-life fission-product poisoning, • Burn-up and breeding effects, • Reflector gain, • Fuel and moderator temperature feed-back, • Control rod effect; • ...

12. Power and Reactivity • Control of Power • Power distribution can be controlled both • At the design stage (assembly and core layout, burnable poisons, reflector, reloading strategy), • In operation (mainly by control rods positioning); • Several strategies of control rod management can be adopted (e.g., in French PWRs : A mode, G mode, X mode).

13. Power and Reactivity • Control of Power • Core design and operation : Typical MOX reloading strategy

14. Power and Reactivity • Control of Power • Core design and operation : X mode operating Control of AO Control of Temperature

15. Power and Reactivity • Control of Reactivity • Reactivity of the core is sensitive to : • Reactor life: • Fuel burn-up, • Breeding process, • Fission-product and actinides build-up, • Burnable poison burn-out, • Short-lifetime fission-product poisoning, • Power and temperature feed-back.

16. Power and Reactivity • Control of Reactivity • Core reactivity is also sensitive to any external perturbation of Boltzmann operator : • Soluble boron concentration change, • Position of control banks, • Power output, • Any incident and/or reactivity accident.

17. Power and Reactivity • Control of Reactivity • In normal operation, reactivity is to be kept constant (no measurable reactivity change); • To guarantee respect of this condition, reactivity NEEDS (sources of reactivity changes and design margins) must be compensated exactly by reactivity AVAILABILITIES (worth of control devices).

18. Power and Reactivity • Control of Reactivity (NEEDS) • Reactivity NEEDS (normal operation) : • Respect of safety criteria, • Respect of margins, • Compensation of fuel burn-up and breeding, • Compensation of burnable poison burn-out, • Compensation of Xenon and Samarium build-up, • Compensation of power and temperature effect.

19. Power and Reactivity • Control of Reactivity (NEEDS) • Criteria and margins • The main objective of a nuclear is producing a cheap energy in safest way; • In order to achieve this goal, design and exploitation of the plant must : • Guarantee respect of the safety criteria at any time, • Maximize energy release from the fuel, according to a given exploitation strategy.

20. Power and Reactivity • Control of Reactivity (NEEDS) • Criteria and margins • In order to guarantee respect of the maximum allowed values (criteria), uncertainty is affected to design parameters; • Uncertainty must account for: • Computational precision (base-data, qualification, ..), • Technology of the fuel (fabrication tolerance, …), • Measurement device precision, • Alea (power tilt, ...); • Margins can also be enforced to account for future changes of loading strategies and new fuel features.

21. Power and Reactivity • Control of Reactivity (NEEDS) • Fuel burn-up and breeding • Fissile isotopes burn-out, • Plutonium build-up, • Minor Actinides build-up, • Fission-Products build-up.

22. Power and Reactivity • Control of Reactivity (NEEDS) • Burnable poison burn-out • Burnable poisons contribute to : • Compensate reactivity, • Flatten core power; • When they disappear : • Fuel reactivity can increase, • Power pick can appear.

23. Power and Reactivity • Control of Reactivity (NEEDS) • Xenon and Samarium build-up • Short-lifetime Fission Products as Xenon and Samarium build-up as a consequence of production of power, • Any power change engenders a variation of their concentrations which affects the reactivity of the system, • Local power variation engender spatial discontinuities in concentration which produce power tilt.

24. Power and Reactivity • Control of Reactivity (NEEDS) • Power and temperature effect : • Doppler broadening of wide epi-thermal resonances: • Fissile isotopes do not contribute significantly to Doppler effect owing to compensation among capture and fission reaction-rates, • Fertile isotopes (mainly U238 and Pu 240) have major contribution to the effect; • Moderator effect : • When moderator density varies, neutron spectrum either hardens-up or soften-down and reactivity changes; • Soluble boron poisoning effect : • When moderator density varies, amount of boron atoms per unit volume is modified.

25. Power and Reactivity • Control of Reactivity (NEEDS) • Power and temperature effect : Doppler broadening • Broadening of epi-thermal resonances of heavy isotopes (at first order, only even ones contribute), • Very fast action (sensitive to temperature changes inside the pellet), • About -3°pcm (1 pcm = 1 E-5) par degree Celsius.

26. Power and Reactivity • Control of Reactivity (NEEDS) • Power and temperature effect : Moderator effect • Variation of the water moderating power (neutron spectrum changes), • Long term action (sensitive to the coolant temperature), • Worth sensitive to isotopic composition of the fuel (stronger for MOX).

27. Power and Reactivity • Control of Reactivity (NEEDS) • Power and temperature effect: Moderator effect Void rate 0 100 UOX MOX Reactivity

28. Power and Reactivity • Control of Reactivity (AVAILABILITIES) • Reactivity AVAILABILITIES (normal operation) : • Soluble boron, • Control and scram clusters : • Black rods, • Gray rods, • Burnable poisons : • Fixed, • Extractable • Extractable poisons.

29. Power and Reactivity • Control of Reactivity (AVAILABILITIES) • Soluble boron • Soluble boron is mainly used to compensate the fuel burn-up, • Power shape is quite insensitive to soluble boron poisoning the primary leg, • Soluble boron worth is very sensitive to fuel nature (ranging from 10 pcm/ppm to 4 pcm/ppm and less), • Concentration of boric acid in primary leg is limited by : • Crystallization (clad rupture), • Moderator density dependence of poisoning effect.

30. Power and Reactivity • Control of Reactivity (AVAILABILITIES) • Control and scram clusters • Control clusters can be either homogeneous (AIC) or mixed (axially heterogeneous B4C - AIC), • If needed, boron in boron carbide can be enriched in B10, • The mixed clusters can be more effective then AIC ones, but they posses the inconvenient to bow-up under pressure of He gas produced by B10 neutron capture.

31. Power and Reactivity • Control of Reactivity (AVAILABILITIES) • Control and scram clusters • Control clusters are used to • Finely adjusting the primary leg output temperature, • Controlling Xe oscillations, • Maintaining AO inside the operating range; • When inserted into the core control clusters cannot must respect a threshold to avoid prompt criticality in presence of a rod-ejection reactivity accident. • They can (partially) contribute to scam.

32. Power and Reactivity • Control of Reactivity (AVAILABILITIES) • Burnable poisons • Burnable poisons are used to : • Compensate fuel burn-out, • Contribute to power flattening; • Burnable poisons can be : • Introduced into guide tubes of some unclustered assemblies (Pyrex), • Integrated to the fuel (Gadolinium Oxide) • Thy engender a spectrum hardening,

33. Power and Reactivity • Control of Reactivity (AVAILABILITIES) • Extractable poisons • Extractable poisons are introduced at beginning of cycle into guide tubes of assemblies not receiving control and safety clusters, • Their position is not axially adjustable (they can be either OUT or IN), • They engender a spectrum hardening, • When they are dropped out, a spectral-shift is produced.

34. Reactor Kinetics • Neutron Balance Equation of a multiplying system at time t[inhomogeneous equation]:

35. Reactor Kinetics • Lifecycle inside a reactor system (recall) Production Capture Neutrons Diffusion Slowing-down Leakage

36. Reactor Kinetics • Lifetime and generation-time (recall) • During transientsprompt-neutron lifetime differs from generation time.

37. Reactor Kinetics • Lifetime and generation-time • Typical values for L / L* • Vacuum 20 mm (L* ) • PWR (UOX) 25 s (L* same) • PWR (UOX - MOX) 10 s " • PWR (MOX) 7 s " • FBR (MOX) 5 s " • Critical sphere (U) 6 ns " • Critical sphere (Pu) 3 ns "

38. Reactor Kinetics • Point Kinetics • Heuristic approach • Reactor is homogenized in space and collapsed to a space-point system (no explicit dependence of variables on space), • Neutrons are collapsed in energy to one group (no explicit dependence of neutrons on energy), • Simplified statistical approach: • The number of neutron in the system is quite large, • The behavior of the system is described by averaged values of reaction-rates.

39. Reactor Kinetics • Point Kinetics • Heuristic approach : Principle • A quite simple demography problem where, every generation-time L, the neutron population is multiplied by a factor • In a conventional PWR there are about 40 neutron generations per millisecond, i.e. 40 000 per second. • Time Neutron population • 0 N0 • L N0 * • 2L N0 * * • 3L N0 * * *

40. Reactor Kinetics • Point Kinetics • Heuristic approach : Application • Keff = 1.00010 L= 25s • Neutron generation per second = 1/25E-6 = 40 000 • Time (s) Neutron population • 0 N0 • 1 N0*E+40 000 = N0*55 • 2 N0*E+80 000 = N0*2980 • 3 N0*E+120 000 = N0*162 000 • Simple but catastrophic scenario!

41. Reactor Kinetics • Point Kinetics • Heuristic approach : Application • Keff = 0.900 L= 25s • Neutron generation per millisecond = 1E-3/25E-6 = 40 • Time (ms) Neutron population • 0 N0 • 1 N0*E+40 = N0*0.0150 • 2 N0*E+80 = N0*0.0002 • 3 N0*E+120 = N0*0.000003 • Simple but catastrophic scenario!

42. Reactor Kinetics • Point Kinetics • Heuristic approach : Sub-critical system with external source • Gain amplifying factor • Time Neutron population • L S • 2L S(1+ ) • 3L S(1+ + * ) • 4L ………

43. Reactor Kinetics • Delayed neutrons • Stability of the nucleus : • The Electromagnetic field inside nucleus : • Effect on protons, • The Nuclear Force field : • Contribution of neutrons to nucleus stability, • The Fission process : • Compound activated nucleus, • Production of fission fragments (Fission Products) • Neutron emission.

44. Reactor Kinetics • Delayed neutrons • Delayed neutron fraction per fission (UOX fuel) : • U235 0.65% • U238 1.48% • Pu239 0.21% • Delayed neutron emission time : • Br87 -> Kr87 -> Kr86+n 80.6 s • I137 -> Xe137 > Xe136+n 32.8 s

45. Reactor Kinetics • Back to the Fission process Diffusion & slowing-down Incident neutron Delay >0.3 sec Delay>03 sec. Fission Prompt neutrons Delayed neutrons Bv (1-B)v

46. Reactor Kinetics • Point Kinetics • Thermal feed-back : Power and temperature effect (recall): • Doppler broadening : • Fissile isotopes do not contribute significantly to Doppler effect, • Fertile isotopes (mainly U238 and Pu 240) have major contribution to the effect; • Moderator effect : • When moderator changes, neutron spectrum is affected; • Soluble boron poisoning effect : • When moderator density varies, amount of boron atoms per unit volume is modified.

47. Residual Power • Time-dependence • After shut-down, power does not go immediately to zero: • The system undergoes a fast transient during which power decrease is driven by decay of residual neutron precursors (Fission Products) [kinetics], • Afterwards, power goes-on decreasing very slowly [activity, residual power].

48. Residual Power • Sources of activity • Radioactive decay of: • Fission Products (B+y), • U239, Np239 and daughters (B+y), • Minor Actinides (a), • Other Activation Products (B+y), • Spontaneous Fission, • Induced neutron emission.

49. Residual Power • Sources of activity • In order to explain origin of different contributions to the activity, several items must analyzed : • The fuel burn-up breeding process described by Heavy-Isotope Depletion Chain, • The decay process of nuclei described in Base-Data Libraries.

50. Residual Power • Sources of activity • Activity is also due to the multiplication in sub-critical conditions of the inherent neutron source : • Spontaneous Fission, • Neutron emission by Oxygen 18 : • Actinide decay produces a particles, • Free neutrons are generated by stripping by a particles on O18.